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Complex numbers and quadratic equations is a segment of maths that deals with crucial theorems and concepts along with various formulae. It comprises of linear and quadratic equations along with roots related to the complex number's set (known as complex roots)..

Q1. Suppose z1,z2 and z3 represent the vertices A,B and C of an equilateral triangle ABC on the Argand plane. Then, AB = BC = CA
If the complex z1,z2,z3 represent the vertices of an equilateral triangle such that |z1 |=|z2 |=|z3 |, then z1+z2+z3 is equal to
•  0
•  3
•  Ï‰
•  Ï‰2
Solution

Q2.
If arg⁡(z) > 0,then arg⁡(-z)-arg⁡(z) = Î»1 and if arg⁡(z)< 0,then arg⁡(z)-arg⁡(-z) = Î»2, then
•  Î»1+Î»2=0
•  Î»1-Î»2=0
•  3Î»1-2Î»2=0
•  2Î»1-3Î»2=0
Solution

Q3.
The number of integral values of m such that given quadratic equation has imaginary roots, are
•  0
•  1
•  2
•  3
Solution

Q4.
The correct statement (s) is are
I. if Î± and Î² are real and unequal ,then Î» and Î´ are also real.
II. if Î± and Î² are imaginary, then Î» and Î´ are also imaginary.
•  I only
•  II only
•  Both I and II
•  Neither I nor II
Solution

Q5.
The value of p is
•  -3
•  -4
•  4
•  3
Solution

Q6.
The least value of g(x) is
•  -1
•  -1/2
• -1/4
•  -1/3
Solution

Q7.
Complex number z1 ¯z2 is
•  Purely real
•  Purely imaginary
•  Zero
•  None of these
Solution

(b)
Q8.
The value of Î¸ for which z is purely real are
•  nÏ€-Ï€/4 , n∈I
•  nÏ€+Ï€/4 , n∈I
•  nÏ€ , n∈I
•  None of these
Solution
(a)

Q9. Consider a quadratic equation az^2+bz+c=0 where a,b,c are complex numbers
The condition that the equation has one purely imaginary root is
•
•
•
•
Solution
(a)

Q10. Consider the equation az+b¯z+c=0, where a,b ,c∈Z
If |a|≠|b|, then z represents

•  Circle
•  Straight line
•  One point
• Ellipse
Solution

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